Characteristics of quadratics

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What shape does the graph of a quadratic function form?

Back

The graph of a quadratic function forms a parabola.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x for which f(x) = 0; they are the points where the graph intersects the x-axis.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

What does the axis of symmetry represent in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, and it passes through the vertex.

Front

How can you find the axis of symmetry for a quadratic function in standard form?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation ax² + bx + c.

Front

What is the difference between maximum and minimum in the context of quadratics?

Back

A maximum is the highest point of a parabola that opens downwards, while a minimum is the lowest point of a parabola that opens upwards.

Front

What are the y-intercepts of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as ax² + bx + c = 0.

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is written as f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots or zeros of the function.